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Anonymous

This is from the Statistics for the behavioral and social sciences text book.

I already did number 1 but I do not understand number two.

For the planned contrast, the null hyp Researchers are investigating the need for mental health care among inmates of three different types of prison facilities. The researchers randomly select 4747 prisoners from each type of facility and report the following conclusions. "The need for mental health care among prisoners in the three types of prison systems appeared to be clearly different, F(2,138138)=5.65<0.01. A planned contrast of System 1 to System 2 was significant, F(1,138138)=4.16<0.05."

Explain this result to a person who has never had a course in statistics.1. The null hypothesis is that the three groups are from populations of number of prisoners needing mental health care with equal means. If this null hypothesis is true, the variance of these populations can be estimated in two ways. (i) Estimate from the variation within each of the three groups and then average them. (ii) Estimate from the variation between the three means, multiplying by the size of each sample group. Since the estimates should be approximately equal, the ratio of the two estimates should be approximately 1. If the null hypothesis is false, the estimate (ii) is greater than the estimate (i) and the ratio, F, of (i) to (ii) is greater than 1. The fact that F=5.65 is much larger than 1 and <0.01 indicates that the null hypothesis can be rejected.

2. For the planned contrast, the null hypothesis is that System 1 and System 2 are from populations of number of prisoners needing mental health care with equal means. If this null hypothesis is (true or false) the variance of these populations can be estimated in two ways. (i) Estimate from the variation within each of the (two or three) groups and then (sum or average) them. (ii) Estimate from the variation between the (two or three) means, by the size of each sample group. Since the estimates should be approximately equal, the ratio of the two estimates should be approximately 1. If the null hypothesis is (true or false) the estimate (ii) is (less or greater) than the estimate (i) and the ratio, F, of (i) to (ii) is (less or greater) than 1. The fact that F=4.16 is much larger than 1 and p<0.05 indicates that the null hypothesis (can or cannot) be rejected.

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